Solve 26x^2-11x-12=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{2}, x_{2} = \frac{12}{13}

Alternative Form

x_{1} = - 0.5, x_{2} = 0. \dot{9} 2307 \dot{6}

Evaluate

26 x^{2} - 11 x - 12 = 0

Factor the expression

More Steps

Evaluate

26 x^{2} - 11 x - 12

Rewrite the expression

26 x^{2} + (- 24 + 13) x - 12

Calculate

26 x^{2} - 24 x + 13 x - 12

Rewrite the expression

2 x \times 13 x - 2 x \times 12 + 13 x - 12

Factor out 2 x from the expression

2 x (13 x - 12) + 13 x - 12

Factor out 13 x - 12 from the expression

(2 x + 1) (13 x - 12)

(2 x + 1) (13 x - 12) = 0

When the product of factors equals 0,at least one factor is 0

13 x - 12 = 0 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

13 x - 12 = 0

Move the constant to the right-hand side and change its sign

13 x = 0 + 12

Removing 0 doesn't change the value,so remove it from the expression

13 x = 12

Divide both sides

\frac{13 x}{13} = \frac{12}{13}

Divide the numbers

x = \frac{12}{13}

x = \frac{12}{13} 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 1 = 0

Move the constant to the right-hand side and change its sign

2 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{2}

x = \frac{12}{13} x = - \frac{1}{2}

Solution

x_{1} = - \frac{1}{2}, x_{2} = \frac{12}{13}

Alternative Form

x_{1} = - 0.5, x_{2} = 0. \dot{9} 2307 \dot{6}

Show Solution